Such saw blades, or put more generally also blade-like parting or cutting tools with a peripherally cutting chip area, are used e.g. in the medical field, as well as in precision mechanics, aircraft construction, ship building, microelectronics and for cutting composite materials. For the particularly demanding and delicate use in bone surgery e.g. microsaws with teeth set to the left and right or further developments with no such offset teeth arrangement are known from German patent 32 22 339. However, these known cutting tools suffer from significant disadvantages. They are generally small tools for precision working, which are e.g. manufacturable by etching or laser technology. A particularly simple and rational manufacture of saw blades by etching leads to the formation of pores and unevennesses on the surface. A surface which is uneven and has pores is very disadvantageous for surgical applications, where working has to take place in a completely sterile manner, because bacteria and germs can be deposited in the unevennesses, which makes the necessary sterilization very difficult. A further disadvantage is the lack of slidability on the part of known saw blades. It is very important in the case of demanding parting cuts in delicate materials and in particular in bone surgery to reduce the friction on the material and therefore produce a minimum of heating in sensitive bone material, so as to prevent thermonecrosis. For this purpose it is necessary to detect at an early stage any wear and therefore blunting of the cutting tool.